A proper orthogonal decomposition technique for the computation of nonlinear panel response

Mortara, Sean; Slater, J. C.; Beran, Philip S.

doi:10.2514/6.2000-1396

Cited by 9 publications

(3 citation statements)

References 5 publications

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“…Modes were generated as described by Eqs (9)(10)(11)(12)(13)(14) and ranked, in the traditional manner, by decreasing eigenvalue. The first 24 modes were kept for the analyses, and four reduced-order model simulations were 6, while Fig.…”

Section: Resultsmentioning

confidence: 99%

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In‐Situ Residual Tracking in Reduced Order Modelling

Slater

Pettit

Beran

2001

Shock and Vibration

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Proper orthogonal decomposition (POD) based reduced-order modelling is demonstrated to be a weighted residual technique similar to Galerkin's method. Estimates of weighted residuals of neglected modes are used to determine relative importance of neglected modes to the model. The cumulative effects of neglected modes can be used to estimate error in the reduced order model. Thus, once the snapshots have been obtained under prescribed training conditions, the need to perform full-order simulations for comparison is eliminates. This has the potential to allow the analyst to initiate further training when the reduced modes are no longer sufficient to accurately represent the predominant phenomenon of interest. The response of a fluid moving at Mach 1.2 above a panel to a forced localized oscillation of the panel at and away from the training operating conditions is used to demonstrate the evaluation method.

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Section: Resultsmentioning

confidence: 99%

“…which can be simulated in time, using larger time steps [2,17,13] than the original equations of motion, with the intention of obtaining results functionally equivalent to those that would have been obtained from a full-order model simulation.…”

Section: Galerkin's Methods Applied To a Set Of 1st Order Odesmentioning

confidence: 99%

In‐Situ Residual Tracking in Reduced Order Modelling

Slater

Pettit

Beran

2001

Shock and Vibration

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show abstract

“…POD-based ROMs have also been applied in different forms to problems in many disciplines. Noteworthy achievements with POD-based ROMs include: the development of control models for unsteady flow (Park and Lee, 1998;Rediniotis et al, 1999), airfoil shape optimization Alonso, 2000, 2001), Euler analysis of unsteady flows driven by structural vibration (Pettit and Beran, 2000), and the study of nonlinear oscillations in flexible panels (Mortara and Beran, 2000). A review of relevant work is given by Beran and Silva, 2001.…”

Section: Introductionmentioning

confidence: 99%